Bremermann’s Limit , named after Hans-Joachim Bremermann , is the maximum computational speed of a self-contained system in the material universe. It is derived fromEinstein’s mass-energy equivalency and the Heisenberg uncertainty principle , and is c 2 / h ≈ 1.36 × 10 50 bits per second per kilogram.This value is important when designingcryptographic algorithms, as it can be used to determine the minimum size ofencryption keys or hash values required to create an algorithm that could never be cracked by abrute-force search.
For example, a computer with the mass of the entireEarth operating at the Bremermann’s limit could perform approximately 10 75 mathematical computations per second. If we assume that a cryptographic key can be tested with only one operation, then a typical 128 bit key could be cracked in under 10 −36 seconds. However, a 256 bit key (which is already in use in some systems) would take about two minutes to crack. Using a 512 bit key would increase the cracking time to approaching 10 72 years, without increasing the time for encryption by more than a constant factor (depending on the encryption algorithms used).
The limit has been further analysed in later literature as the maximum rate at which a system with energy spread can evolve into an orthogonal and hence distinguishable state to another, .In particular,Margolus and Levitin has shown that a quantum system with average energy E takes at least time to evolve into an orthogonal state.